On dd-symmetric classical dd-orthogonal polynomials

The dd-symmetric classical dd-orthogonal polynomials are an extension of the standard symmetric classical polynomials according to the Hahn property. In this work, we give some characteristic properties for these polynomials related to generating functions and recurrence-differential equations. As applications, we characterize the dd-symmetric classical dd-orthogonal polynomials of Boas-Buck type, we construct a (d+1)(d+1)-order linear differential equation with polynomial coefficients satisfied by each polynomial of a dd-symmetric classical dd-orthogonal set and we show that the dd-symmetric classical dd-orthogonal property is preserved by the derivative operator. Some of the obtained properties appear to be new, even for the case d=1d=1.